2. Simplifying Radical Expressions

3. Product Property of Radicals For any numbers a and b where and,

4. Product Property of Radicals Examples

5. Examples:

7. Quotient Property of Radicals For any numbers a and b where and,

8. Examples:

10. Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator. Ex: Simplify

11. Simplest Radical Form No perfect nth power factors other than 1. No fractions in the radicand. No radicals in the denominator.

12. Examples:

14. Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

15. Examples:

17. Multiplying radicals - Distributive Property

18. Multiplying radicals - FOIL F O I L

19. Examples: F O I L

20. F O I L

21. Conjugates Binomials of the form where a, b, c, d are rational numbers.

22. The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

23. Examples: